Ploidacot/Dicot: Difference between revisions
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{{Breadcrumb}} | {{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=0|Cots=2|Pergen=[P8, P5/2]|Forms=7, 10, 17|Title=Dicot|Wedgie=2}} | ||
'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments tend to involve "neutral" intervals, which are in-between conventional diatonic intervals. | '''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments tend to involve "neutral" intervals, which are in-between conventional diatonic intervals. | ||
== Intervals and notation == | == Intervals and notation == | ||
Dicot temperaments can be notated using [[Neutral chain-of-fifths notation|neutral chain-of-fifths notation | Dicot temperaments can be notated using [[Neutral chain-of-fifths notation|neutral chain-of-fifths notation]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Dicot intervals (assuming pure fifth and octave) | |+ style="font-size: 105%;" | Dicot intervals (assuming pure fifth and octave) | ||
!# | |- | ||
!Cents | ! # | ||
!Notation | ! Cents | ||
!Name | ! Notation | ||
! Name | |||
|- | |- | ||
| | | −10 | ||
|90.22 | | 90.22 | ||
|Db | | Db | ||
|minor second | | minor second | ||
|- | |- | ||
| | | −9 | ||
|441.20 | | 441.20 | ||
|Fd | | Fd | ||
|semidiminished fourth | | semidiminished fourth | ||
|- | |- | ||
| | | −8 | ||
|792.18 | | 792.18 | ||
|Ab | | Ab | ||
|minor sixth | | minor sixth | ||
|- | |- | ||
| | | −7 | ||
| | | 1143.16 | ||
|Cd | | Cd | ||
|semidiminished octave | | semidiminished octave | ||
|- | |- | ||
| | | −6 | ||
|294. | | 294.13 | ||
|Eb | | Eb | ||
|minor third | | minor third | ||
|- | |- | ||
| | | −5 | ||
|645.11 | | 645.11 | ||
|Gd | | Gd | ||
|semidiminished fifth | | semidiminished fifth | ||
|- | |- | ||
| | | −4 | ||
|996.09 | | 996.09 | ||
|Bb | | Bb | ||
|minor seventh | | minor seventh | ||
|- | |- | ||
| | | −3 | ||
|147.07 | | 147.07 | ||
|Dd | | Dd | ||
|neutral second | | neutral second | ||
|- | |- | ||
| | | −2 | ||
|498. | | 498.04 | ||
|F | | F | ||
|perfect fourth | | perfect fourth | ||
|- | |- | ||
| | | −1 | ||
|849.02 | | 849.02 | ||
|Ad | | Ad | ||
|neutral sixth | | neutral sixth | ||
|- | |- | ||
|0 | | 0 | ||
|0 | | 0 | ||
|C | | C | ||
|perfect unison | | perfect unison | ||
|- | |- | ||
|1 | | 1 | ||
|350.98 | | 350.98 | ||
|Ed | | Ed | ||
|neutral third | | neutral third | ||
|- | |- | ||
|2 | | 2 | ||
|701.96 | | 701.96 | ||
|G | | G | ||
|perfect fifth | | perfect fifth | ||
|- | |- | ||
|3 | | 3 | ||
| | | 1052.93 | ||
|Bd | | Bd | ||
|neutral seventh | | neutral seventh | ||
|- | |- | ||
|4 | | 4 | ||
|203.91 | | 203.91 | ||
|D | | D | ||
|major second | | major second | ||
|- | |- | ||
|5 | | 5 | ||
|554.89 | | 554.89 | ||
|Ft | | Ft | ||
|semiaugmented fourth | | semiaugmented fourth | ||
|- | |- | ||
|6 | | 6 | ||
|905.87 | | 905.87 | ||
|A | | A | ||
|major sixth | | major sixth | ||
|- | |- | ||
|7 | | 7 | ||
|56.84 | | 56.84 | ||
|Ct | | Ct | ||
|semiaugmented unison | | semiaugmented unison | ||
|- | |- | ||
|8 | | 8 | ||
|407.82 | | 407.82 | ||
|E | | E | ||
|major third | | major third | ||
|- | |- | ||
|9 | | 9 | ||
|758.80 | | 758.80 | ||
|Gt | | Gt | ||
|semiaugmented fifth | | semiaugmented fifth | ||
|- | |- | ||
|10 | | 10 | ||
| | | 1109.78 | ||
|B | | B | ||
|major seventh | | major seventh | ||
|} | |} | ||
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=== Dicot === | === Dicot === | ||
The temperament named "[[dicot]]" is an exotemperament, equating the neutral third to 5/4. This means that 6/5 is the same interval, and the neutral sixth represents both 5/3 and 8/5. It is best tuned with either a sharpened generator of around 360 | The temperament named "[[dicot]]" is an exotemperament, equating the neutral third to 5/4. This means that 6/5 is the same interval, and the neutral sixth represents both 5/3 and 8/5. It is best tuned with either a sharpened generator of around 360{{c}} (optimizing for the tuning of 5/4) or a flattened generator of around 340{{c}} (optimizing for the tuning of 5/3). | ||
=== Neutral === | === Neutral === | ||
[[Neutral]] is the temperament equating [[11/9]] with [[27/22]]. This makes 11/9 the neutral third and [[11/8]] the semiaugmented fourth. | [[Neutral (temperament)|Neutral]] is the temperament equating [[11/9]] with [[27/22]]. This makes 11/9 the neutral third and [[11/8]] the semiaugmented fourth. [[Namo]] extends neutral so that [[16/13]] is found at the same neutral third. Namo is often used as an 11- and 13-limit extension of other temperaments. | ||
=== Mohajira === | === Mohajira === | ||
When neutral is combined with [[meantone]] (which sets the major third equal to [[5/4]]), the result is [[mohajira]], which tunes the generator of ~11/9 to about 348 | When neutral is combined with [[meantone]] (which sets the major third equal to [[5/4]]), the result is [[mohajira]], which tunes the generator of ~11/9 to about 348{{c}} and extends to the full 11-limit by setting 7/4 equal to the semidiminished seventh. | ||
=== Hemififths === | === Hemififths === | ||
Fittingly to its name, [[hemififths]] divides the fifth evenly into two [[49/40]]~[[60/49]]<nowiki/>s. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented ( | Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second. | ||
[[Category:Ploidacots|Dicot]] | |||